Reply to a revised comment on"Why is the DNA denaturation transition first order?"

1 Kafri, Mukamel, and Peliti Reply: The Comment of Hanke and Metzler [1] questions the validity of the analysis presented in [2] to DNA chains of finite length as used in experiments. Their argument is that for the analysis to be valid " each of the three segments going out of a vertex must be much longer than the persistence length ℓ p of this segment ". By using the persistence lengths ℓ p (L) ∼ 40Å for a single strand and ℓ p (H) ∼ 500Å for a double helix (bound segment) they arrive at the conclusion that in order to observe the asymptotic behavior found in [2] one needs chains which are far longer than those studied experimentally. This assertion is a consequence of a misinterpretation of the analysis given in [2]. In this analysis one considers a loop interacting with the rest of the chain and not just with the vicinal double helices. Thus, in [2] each of the two lines attached to the loop is in fact composed of an alternating sequence of bound segments and denaturated loops. It may be viewed as a stick-and-joint structure, whereby adjacent double helices are loosely attached to each other via an open loop. The " rest of the chain " as considered in reference [2] is in fact a jointed rods structure with a persistence length which is given by ℓ p (H) when the distance between loops, ξ, is larger than ℓ p (H) and is given by ξ when ξ < ℓ p (H). In the Comment the authors claim that the analysis of [2] is valid only when the helical segment is flexible and thus much larger than the persistence length ℓ p (H), where it could be described by a self-avoiding walk. This claim is incorrect. The analysis is valid as long as the chain contains a sufficient number of loops to allow considering the stick-and-joint structure (Fig. 1) as a self-avoiding walk. Thus, even short chains of length of the order of 5000 base pairs could allow for about 20 joints which is large enough to make the analysis of [2] valid. This is clearly evident from experimental melting curves [3, 4] of chains of such lengths. These curves exhibit over 10 individual sub transitions corresponding to the existence of a large number of loops (since some of the peaks correspond to more than …